How to find out if lines are parallel - GRE Quantitative Reasoning
Card 0 of 7
Which of the following lines is parallel to:
Which of the following lines is parallel to:
First write the equation in slope intercept form. Add 
to both sides to get 
. Now divide both sides by 
to get 
. The slope of this line is 
, so any line that also has a slope of 
would be parallel to it. The correct answer is 
.
First write the equation in slope intercept form. Add
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There are two lines:
2x – 4y = 33
2x + 4y = 33
Are these lines perpendicular, parallel, non-perpendicular intersecting, or the same lines?
There are two lines:
2x – 4y = 33
2x + 4y = 33
Are these lines perpendicular, parallel, non-perpendicular intersecting, or the same lines?
To be totally clear, solve both lines in slope-intercept form:
2x – 4y = 33; –4y = 33 – 2x; y = –33/4 + 0.5x
2x + 4y = 33; 4y = 33 – 2x; y = 33/4 – 0.5x
These lines are definitely not the same. Nor are they parallel—their slopes differ. Likewise, they cannot be perpendicular (which would require not only opposite slope signs but also reciprocal slopes); therefore, they are non-perpendicular intersecting.
To be totally clear, solve both lines in slope-intercept form:
2x – 4y = 33; –4y = 33 – 2x; y = –33/4 + 0.5x
2x + 4y = 33; 4y = 33 – 2x; y = 33/4 – 0.5x
These lines are definitely not the same. Nor are they parallel—their slopes differ. Likewise, they cannot be perpendicular (which would require not only opposite slope signs but also reciprocal slopes); therefore, they are non-perpendicular intersecting.
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Which pair of linear equations represent parallel lines?
Which pair of linear equations represent parallel lines?
Parallel lines will always have equal slopes. The slope can be found quickly by observing the equation in slope-intercept form and seeing which number falls in the "
" spot in the linear equation 
,
We are looking for an answer choice in which both equations have the same value. Both lines in the correct answer have a slope of 2, therefore they are parallel.
Parallel lines will always have equal slopes. The slope can be found quickly by observing the equation in slope-intercept form and seeing which number falls in the "
We are looking for an answer choice in which both equations have the same
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Which of the following equations represents a line that is parallel to the line represented by the equation 
?
Which of the following equations represents a line that is parallel to the line represented by the equation
Lines are parallel when their slopes are the same.
First, we need to place the given equation in the slope-intercept form.
Because the given line has the slope of 
, the line parallel to it must also have the same slope.
Lines are parallel when their slopes are the same.
First, we need to place the given equation in the slope-intercept form.
Because the given line has the slope of
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Which of the above-listed lines are parallel?
Which of the above-listed lines are parallel?
There are several ways to solve this problem. You could solve all of the equations for 
. This would give you equations in the form 
. All of the lines with the same 
value would be parallel. Otherwise, you could figure out the ratio of 
to 
when both values are on the same side of the equation. This would suffice for determining the relationship between the two. We will take the first path, though, as this is most likely to be familiar to you.
Let's solve each for 
:
Here, you need to be a bit more manipulative with your equation. Multiply the numerator and denominator of the 
value by 
:
Therefore, 
, 
, and 
all have slopes of 
There are several ways to solve this problem. You could solve all of the equations for
Let's solve each for
Here, you need to be a bit more manipulative with your equation. Multiply the numerator and denominator of the
Therefore,
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Which of the following is parallel to the line passing through 
and 
?
Which of the following is parallel to the line passing through
Now, notice that the slope of the line that you have been given is 
. You know this because slope is merely:
However, for your points, there is no rise at all. You do not even need to compute the value. You know it will be 
. All lines with slope 
are of the form 
, where 
is the value that 
has for all 
points. Based on our data, this is 
, for 
is always 
—no matter what is the value for 
. So, the parallel answer choice is 
, as both have slopes of 
.
Now, notice that the slope of the line that you have been given is
However, for your points, there is no rise at all. You do not even need to compute the value. You know it will be
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Which of the following is parallel to 
?
Which of the following is parallel to
To begin, solve your equation for 
. This will put it into slope-intercept form, which will easily make the slope apparent. (Remember, slope-intercept form is 
, where 
is the slope.)
Divide both sides by 
and you get:
Therefore, the slope is 
. Now, you need to test your points to see which set of points has a slope of 
. Remember, for two points 
and 
, you find the slope by using the equation:
For our question, the pair 
and 
gives us a slope of 
:
To begin, solve your equation for
Divide both sides by
Therefore, the slope is
For our question, the pair
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